Question

In about $1657,$ Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P14.54). Two teams of eight horses each could pull the hemispheres apart only on some trials and then "with greatest difficulty," with the resulting sound likened to a cannon firing. Find the force $F$ required to pull the thinwalled evacuated hemispheres apart in terms of $R,$ the radius of the hemispheres; $P$, the pressure inside the hemispheres; and atmospheric pressure $P_{0}$. (FIGURE CANT COPY)

Name: Problem 54, Chapter 14: Physics For Scientist and Engineers with Modern Physics
Uploaded: 2020-06-04T10:11:21-08:00
Duration: 51 s
Channel: Mayukh Banik

   In about $1657,$ Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P14.54). Two teams of eight horses each could pull the hemispheres apart only on some trials and then "with greatest difficulty," with the resulting sound likened to a cannon firing. Find the force $F$ required to pull the thinwalled evacuated hemispheres apart in terms of $R,$ the radius of the hemispheres; $P$, the pressure inside the hemispheres; and atmospheric pressure $P_{0}$.
(FIGURE CANT COPY)

Physics For Scientist and Engineers with Modern Physics

Raymond A. Serway,… 4th Edition

Chapter 14, Problem 54

Instant Answer

Solved by Expert Mayukh Banik

06/04/2020

Step 1

The problem involves calculating the force required to pull apart two evacuated hemispheres. The force required is due to the atmospheric pressure acting on the outside of the hemispheres while there is a lower pressure (or vacuum) inside. Show more…

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In about $1657,$ Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P14.54). Two teams of eight horses each could pull the hemispheres apart only on some trials and then "with greatest difficulty," with the resulting sound likened to a cannon firing. Find the force $F$ required to pull the thinwalled evacuated hemispheres apart in terms of $R,$ the radius of the hemispheres; $P$, the pressure inside the hemispheres; and atmospheric pressure $P_{0}$. (FIGURE CANT COPY)

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Key Concepts

Force from Pressure Integration

When a pressure difference acts over an area, the resulting force can be determined by multiplying the pressure difference by the area. In the case of the evacuated sphere, the force required to pull apart the hemispheres is calculated as F = (P? - P)?R², where P? is the atmospheric pressure and P is the internal pressure.

Projected Area

In dealing with forces due to pressure, one typically integrates the pressure over a specific area. For spherical objects, the effective area that contributes to the separation force is the circular cross-sectional area, which is given by ?R², where R is the radius.

Pressure Difference

This concept refers to the difference between the external atmospheric pressure and the internal pressure of a system. In many physical scenarios, especially those involving vacuums or evacuated spaces, it is the net pressure pushing on a surface that produces force.

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